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This paper is a further development of a previous work (PAMM 16, 51–52). In this paper, we derive an analytical formulation of the linear actuators’ length variations for a 2-1-2 DOF joint designed parallel hexapod based on Riebe and Ulbrich’s method (Arch. Appl. Mech. 72, 817–829) and the Euler angles based matrix method. The equivalence conditions as well as the computation errors are given and compared with a quaternion based method.

Comparison of Three Methods of Length Compensation in a Parallel Kinematic and Their Equivalence Conditions